Geodesic
Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view
Journal of Singularities, Tome 18 (2018), pp. 409-426

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This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called "Prony system". We provide a short overview of its unusually wide connections with many different fields of Mathematics, stressing the role of Singularity Theory. We reformulate Prony System as the problem of reconstruction of "Spike-train" signals from the noisy moment measurements. We provide an overview of some recent results on the "geometry of the error amplification" in the reconstruction process, in situations where the nodes x_j near-collide. Some algebraic-geometric structures, underlying the error amplification, are described (Prony, Vieta, and Hankel mappings, Prony varieties), as well as their connection with Vandermonde mappings and varieties. Our main goal is to present some promising fields of possible applications of Singularity Theory. 
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     author = {Gil Goldman and Yehonatan Salman, and Yosef Yomdin},
     title = {Accuracy of noisy {Spike-Train} {Reconstruction:} a {Singularity} {Theory} point of view},
     journal = {Journal of Singularities},
     pages = {409--426},
     publisher = {mathdoc},
     volume = {18},
     year = {2018},
     doi = {10.5427/jsing.2018.18u},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18u/}
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Gil Goldman; Yehonatan Salman,; Yosef Yomdin. Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view. Journal of Singularities, Tome 18 (2018), pp. 409-426. doi: 10.5427/jsing.2018.18u

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